This paper investigates the conditions under which diagonal sentences can be taken to constitute paradigmatic cases of self-reference. We put forward well-motivated constraints on the diagonal operator and the coding apparatus which separate paradigmatic self-referential sentences, for instance obtained via Gödel’s diagonalization method, from accidental diagonal sentences. In particular, we show that these constraints successfully exclude refutable Henkin sentences, as constructed by Kreisel.
CITATION STYLE
Grabmayr, B., Halbach, V., & Ye, L. (2023). Varieties of Self-Reference in Metamathematics. Journal of Philosophical Logic, 52(4), 1005–1052. https://doi.org/10.1007/s10992-022-09696-y
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